That's a ridiculous twist of words. That's not self-insured, it's just planning for loss, which is exactly what it's called (Unplanned expenditures).

No it's not. If you book it under "Unplanned expenditures" then you're not insured. If you try to determine your risk in such a way that you can budget a fixed sum for coverage and reasonably expect not to exceed it (ie. not an unplanned expenditure) in the same way an insurance company would do it, they you're insured.

It's literally a line item in the budget for unplanned expenditures. Sounds ridiculous, but you are planning for the unplanned. I'm just saying calling that "insurance" dilutes the meaning of what insurance actually is, which requires a transaction between two separate companies.